# Obtaining a two step transition matrix in a stationary Markov chain

I'm reading the chapter on Markov processes in DeGroot and do not find the explanation for the following thing:

A transition matrix P is specified in the following way: $$P = \begin{pmatrix} 0.1 & 0.4 & 0.2 & 0.1 & 0.1 & 0.1\\ 0.2 & 0.3 & 0.2 & 0.1 & 0.1 & 0.1\\ 0.1 & 0.2 & 0.3 & 0.2 & 0.1 & 0.1\\ 0.1 & 0.1 & 0.2 & 0.3 & 0.2 & 0.1\\ 0.1 & 0.1 & 0.1 & 0.2 & 0.3 & 0.2\\ 0.1 & 0.1 & 0.1 & 0.1 & 0.4 & 0.2 \end{pmatrix}$$

And mentions that to obtain a two step matrix you simply multiply the matrix by itself to obtain $P^2$.

I don't understand how these values are obtained for $P^2$: $$P = \begin{pmatrix} 0.14 & 0.23 & 0.20 & 0.15 & 0.16 & 0.12\\ 0.13 & 0.24 & 0.20 & 0.15 & 0.16 & 0.12\\ 0.12 & 0.20 & 0.21 & 0.18 & 0.17 & 0.12\\ 0.11 & 0.17 & 0.19 & 0.20 & 0.20 & 0.13\\ 0.11 & 0.16 & 0.16 & 0.18 & 0.24 & 0.15\\ 0.11 & 0.16 & 0.15 & 0.17 & 0.25 & 0.16 \end{pmatrix}$$

What am I missing? Should the values simply be multiplied by themselves?

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Welcome to the site. It is preferred that you typeset the math stuff instead of linking it to a file. You can find useful help on how to typeset math here (meta.math.stackexchange.com/questions/107/…) –  user17762 Oct 18 '11 at 15:59

If I understand the question correctly, what you're looking for is matrix multiplication.

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